divisor(n)

Calculate the distinct divisors of a number not just the prime factors.

Description

divisor(n) : row vector of all distinct divisors of a positive integer N, including 1 and N.

Remark:
   This function uses the default factor() routine in Matlab and hence is limited to input values up to 2^32. However if factor() routine does get updated for larger integers, this function will still work fine. Alternately you may comment out the statement that compares the values to 2^32, the factor() routine will work just fine (except maybe it will be bit slower for big numbers).
   Using factor() provides a significant speed improvement over manually searching for the each divisor of n.

Example:
   a = divisor(12);
   returns -> a = [1, 2, 3, 4, 6, 12];

See Also:
  factor, primes

• MATLAB release: MATLAB 5.2 (R10)

[Jos (10584)]

For another implementation, see
http://www.mathworks.com/matlabcentral/fileexchange/3944

[Yash]

@ Jos : Thank you for pointing that out. Here's a small code that I wrote to compare the two techniques,

N = 100000;
tic
for i = 1:N
    x = factor2(i);
end
toc

tic
for i = 1:N
    x = divisor(i);
end
toc

On my machine i get the following results,
N = 1000
Elapsed time is 0.022092 seconds.
Elapsed time is 0.203660 seconds.
N = 10000
Elapsed time is 0.869049 seconds.
Elapsed time is 0.809918 seconds.
N = 100000
Elapsed time is 63.062130 seconds.
Elapsed time is 8.858714 seconds.

As you see for large N there is significant increase in speed if we use divisor() instead of factor2()

My take at why factor2() is slow for large N is because it creates an array a = [1:floor(k/2)]; and then removes unnecessary value of a, which is very inefficient way of doing it.

At the least the speed and memory requirement can be improved by modifying factor2() by only searching for factors till sqrt(k), i.e.
a = 1:sqrt(k); % no need to floor (sqrt(k))
and then at the end of code add a = [a, k./a(end:-1:1)]
We will need to check if k is perfect square though.
Here's what I am talking about,
sqk = sqrt(k);
a = 1:sqk;
tmp = k./a;
tmp = isinteger(tmp);
a = a(tmp);
if isinteger(sqk)
    a = [a, k./a(end-1:-1:1)];
else
    a = [a, k./a(end:-1:1)];
end

This implementation will be much better than the previous factor2(). In fact it will be much better than divisor() for small N.